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For instance,

dy/dx + 3y = exp(-x) + exp(-3x)

y(CF) = Aexp(−3x)

y(PI) = Cexp(−x) + D

**exp(−3x)**

__x__The term Dexp(-3x) in the P.I. has to be multiplied by

**to be linearly independent of Aexp(-3x) in the C.F.. Why? What would happen if it wasn't?**

__x__